comp.risk {timereg}R Documentation

Competings Risks Regression

Description

Fits a semiparametric model for the cause-specific quantities :

P(T <=q t, cause=1 | x,z) = P_1(t,x,z) = h( - g(t,x,z) )

for a known link-function h() and known prediction-function g(t,x,z) for the probability of dying from cause 1 in a situation with competing causes of death.

We consider the following models : 1) the additive model where h(x)=1-exp(x) and

g(t,x,z) = x^T A(t) + (diag(t^p) z)^T β

2) the proportional setting that includes the Fine & Gray (FG) model and some extensions where h(x)=1-exp(-exp(x)) and

g(t,x,z) = exp(x^T A(t) + (diag(t^p) z)^T β)

The FG model is obtained when x=1.

3) a logistic model where h(x)=exp(x)/( 1+exp(x)) and

g(t,x,z) = x^T A(t) + (diag(t^p) z)^T β

4) the "1-additive" model where h(x)=exp(x) and

g(t,x,z) = x^T A(t) + (diag(t^p) z)^T β

)

Where p by default is 1 for the additive model and 0 for the other models. In general p may be powers of the same length as z.

Usage

comp.risk(formula,data=sys.parent(),cause,times,Nit=50,
clusters=NULL,gamma=0,n.sim=500,weighted=0,model="additive",
causeS=1,cens.code=0,detail=0,interval=0.01,resample.iid=1,
cens.model="KM",time.pow=0)

Arguments

formula a formula object, with the response on the left of a '~' operator, and the terms on the right. The response must be a survival object as returned by the `Surv' function. The status indicator is not important here. Time-invariant regressors are specified by the wrapper const(), and cluster variables (for computing robust variances) by the wrapper cluster().
data a data.frame with the variables.
cause specifies the causes related to the death times, the value 0 is the censoring value.
times specifies the times at which the estimator is considered. This is typically all cause "1" jump times.
Nit number of iterations for Newton-Raphson algorithm.
clusters specifies cluster structure, for backwards compability.
gamma starting value for constant effects.
n.sim number of simulations in resampling.
weighted Not implemented. To compute a variance weighted version of the test-processes used for testing time-varying effects.
model "additive", "prop"ortional or "logistic".
causeS specificies which cause we consider.
cens.code specificies the code for the censoring.
detail if 0 no details are printed during iterations, if 1 details are given.
interval specifies that we only consider timepoints where the Kaplan-Meier of the censoring distribution is larger than this value.
resample.iid to return the iid decomposition, that can be used to construct confidence bands for predictions
cens.model specified which model to use for the ICPW, KM is Kaplan-Meier alternatively it may be "cox"
time.pow specifies that the power at which the time-arguments is transformed, for each of the arguments of the const() terms, default is 1 for the additive model and 0 for the proportional model.

Value

returns an object of type 'comprisk'. With the following arguments:

cum cumulative timevarying regression coefficient estimates are computed within the estimation interval.
var.cum pointwise variances estimates.
gamma estimate of proportional odds parameters of model.
var.gamma variance for gamma.
score sum of absolute value of scores.
gamma2 estimate of constant effects based on the non-parametric estimate. Used for testing of constant effects.
obs.testBeq0 observed absolute value of supremum of cumulative components scaled with the variance.
pval.testBeq0 p-value for covariate effects based on supremum test.
obs.testBeqC observed absolute value of supremum of difference between observed cumulative process and estimate under null of constant effect.
pval.testBeqC p-value based on resampling.
obs.testBeqC.is observed integrated squared differences between observed cumulative and estimate under null of constant effect.
pval.testBeqC.is p-value based on resampling.
conf.band resampling based constant to construct 95% uniform confidence bands.
B.iid list of iid decomposition of non-parametric effects.
gamma.iid matrix of iid decomposition of parametric effects.
test.procBeqC observed test process for testing of time-varying effects
sim.test.procBeqC 50 resample processes for for testing of time-varying effects

Author(s)

Thomas Scheike

References

Scheike, Zhang and Gerds (2008), Predicting cumulative incidence probability by direct binomial regression, Biometrika.

Scheike and Zhang (2008), Flexible competing risks regression modelling and goodness of fit, LIDA.

Examples

data(bmt); 
times<-bmt$time[bmt$cause==1]; 

add<-comp.risk(Surv(time,cause>0)~platelet+age+tcell,bmt,
bmt$cause,times[-1],causeS=1,resample.iid=1)
summary(add)

par(mfrow=c(2,4))
plot(add); plot(add,score=1)

ndata<-data.frame(platelet=c(1,0,0),age=c(0,1,0),tcell=c(0,0,1))
par(mfrow=c(2,3))
out<-predict(add,ndata,uniform=1,n.sim=100)
par(mfrow=c(2,2))
plot(out,multiple=0,uniform=1,col=1:3,lty=1,se=1)

## fits additive model with some constant effects 
add.sem<-comp.risk(Surv(time,cause>0)~
const(platelet)+const(age)+const(tcell),bmt,
bmt$cause,times[-1],causeS=1,resample.iid=1)
summary(add.sem)

out<-predict(add.sem,ndata,uniform=1,n.sim=100)
par(mfrow=c(2,2))
plot(out,multiple=0,uniform=1,col=1:3,lty=1,se=0)

## Fine & Gray model 
fg<-comp.risk(Surv(time,cause>0)~
const(platelet)+const(age)+const(tcell),bmt,
bmt$cause,times[-1],causeS=1,resample.iid=1,model="prop")
summary(fg)

out<-predict(fg,ndata,uniform=1,n.sim=100)

par(mfrow=c(2,2))
plot(out,multiple=1,uniform=0,col=1:3,lty=1,se=0)

## extended model with time-varying effects
fg.npar<-comp.risk(Surv(time,cause>0)~platelet+age+const(tcell),
bmt,bmt$cause,times[-1],causeS=1,resample.iid=1,model="prop")
summary(fg.npar); 

out<-predict(fg.npar,ndata,uniform=1,n.sim=100)

par(mfrow=c(2,2))
plot(out,multiple=1,uniform=0,col=1:3,lty=1,se=0)

[Package timereg version 1.1-7 Index]